Algorithmic worlds 


Search blog posts20110413 Play with Ducks 20110331 Karl Blossfeldt 20110330 Algorithmic jewellery 20110319 Piling Ducks 20110306 Greco de Ruijter 20110305 Fractal columns 20110228 Kaleidoscopic IFS 20110227 Ducks and butterflies 20110218 Geological artwork 20110217 Fractal expressionism 
BlogA blog about algorithmic art and fractal aesthetic. Click here to subscribe to the RSS feed. February 28th 2011 Kaleidoscopic IFSJust after blogging about Ducks and butterflies, I found out on Fractal Forums about a 3 dimensional analogue of Jonathan McCabe's Butterfly Origami algorithm, named Kaleidoscopic IFS. The idea is explained here, but in French. Still, it might help to look at the picture there to understand the following explanations. We start from a platonic solid. Its symmetry planes define a triangulation of the unit sphere. We pick one of these triangles and consider the three planes intersecting the sphere on its sides. They define a cone with a triangular basis. By a sucession of reflections about the three planes, we can map any point inside this cone. Let's do this. Now we'll perform a sequence of rotations and of translations. If the point gets out of the cone, we use the appropriate combination of reflexions to map it back inside. We iterate the last two steps a certain number of times. Finally, we draw as solid only those points that stayed within a certain distance of the tip of the cone during the whole process. This yields some very cool imagery, and the patterns obtained often looks strikingly similar to their 2d analogues. Here is a bunch of links: Finally here is a very elegant video of an evolving Kaleidoscopic IFS fractal by Tom Beddard, aka subBlue. Surface detail from subBlue on Vimeo. Update: I forgott to mention the original post about Kaleidoscopic IFS fractals on Fractal Forum.


